Studying Of Property Of The Solution For Some Nonlinear Parabolic Equations (Systems)

chemistry, biology and economy, which have strongly practical background;on theother hand, in the studying of nonlinear parabolic equation, many important problemare developed. Therefor, in recent twenties years, the studying of global existence andblow-up for the solution of nonlinear parabolic equations has been a important aspectin the field of nonlinear partial differential equations.This paper mainly concerns thequalitative properties for some nonlinear parabolic equations with initial or initialboundary value, including global existence and blow-up in finite time of solution,thelarge time behavior of global solution and life span of blow-up solutions.In chapter 1, we deal with the Cauchy problem for a degenerate parabolicequation ut = up u + uq. By constructing the self-similar solution and using themethod of super-sub solution and convex, we get a second critical exponent. Precisely,let q > p + 1 + N2 ,a = qp22. If a∈(0,a),u0∈Φa, the solution of problem blow upin finite time; if a∈(a,N),u0 =λφ,φ∈Φa, the solution of problem exist globally.Subsequently, in chapter 2, we continue to discuss the Cauchy problem of de-generate parabolic equationut = up u + uq with decaying initial function in infinitedistant.Exploiting convex method, ordinal differential equation and constructingspecial function, we obtain life span estimation of blow-up solution and the large timebehavior of global solution.